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The recent advances in scintillating materials development have resulted in the availability of LaBr3:Ce and CeBr3 crystals combining fast light decay with high light yield and stopping power. The detectors based on these crystals have energy resolution <3% (for ~1 MeV energy deposition) and sub-nanosecond time resolution. The main factor limiting the use of LaBr3:Ce is its internal background coming from naturally occuring isotope 139La and 237Ac pollution. CeBr3 crystals have much lower background rate. LaBr3:Ce and CeBr3 crystals are planned for use in a future space experiments. In this case a problem of a crystal radiation hardness arises. Considering low orbit experiments a number of factors such as irradiation by galactic and solar cosmic rays, or by protons of inner radiation belt are present. Energetic protons produce also neutrons coming from the Earth atmosphere (albedo neutrons) as well as from the spacecraft intself (local neutrons). Taking into account the difference in background producing reactions by protons and neutrons, as well, as the difference between LaBr3:Ce and CeBr3 composition we performed tests of radiation hardness of LaBr3:Ce and CeBr3 scintillating crystals with the use of a neutron beam at the MedApp and Nectar facilitgy at FRMII. In this presentation we compare results of the fast neutron induced activation of LaBr3:Ce and CeBr3 with doses 10^9-10^12 n/cm2 with that of proton induced activation, as well as an activation due to number of isotopes with half life values from several hours to a hundred days.